The Closed Fragment of the Interpretability Logic of PRA with a Constant for $\mathrm{I}\Sigma_1$
Joost J. Joosten · Notre Dame Journal of Formal Logic · 2005
In this paper we carry out a comparative study of $\mathrm{I}\Sigma_1$ and PRA. We will in a sense fully determine what these theories have to say about each other in terms of provability and interpretability. Our study will result in two arithmetically complete modal logics with simple universal models.